Abstract
In this paper we will prove a criterion for hyperelliptic Jacobians. LetD be a translation invariant vector field on an indecompssable principally polarized abelian variety (i.p.p.a.v.) (X, Θ), letDΘ be the divisor of the sectionDΘ∈H0 (Θ,O(Θ)|Θ). We have that (X, Θ) is the Jacobian of an hyperelliptic curve iff (Theorem 1) all the component ofDΘ are non reduced and the singular locus of Θ has dimension less thang-2.
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